A di erential quadrature procedure for free vibration of rectangular plates involving free corners

Authors

1 Young Researchers and Elite Club, Karaj Branch, Islamic Azad University, Karaj, P.O. Box 31485-313, Iran.

2 Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, P.O. Box 19395-1999, Iran.

Abstract

The Di erential Quadrature Method (DQM) is one of the most powerful approximation methods for analyzing the free vibration of rectangular plates. It is easy to use and straightforward to implement. However, in spite of its many advantages, the conventional DQM has some limitations in determining the natural frequencies of rectangular plates involving free corners. This is because it is very dicult to implement the free corner boundary condition in conventional DQM. As a result, the method may exhibit some convergence problems and this may lead to erroneous and oscillatory results for natural frequencies of rectangular plates involving free corners. To overcome this diculty, this paper presents a simple DQM formulation in which all the natural boundary conditions, including the free corner boundary condition, are implemented in an easy manner. Its accuracy and eciency are demonstrated through the vibration analysis of rectangular plates with di erent combinations of free edges and free corners. Numerical results prove that the proposed method can produce much better accuracy than the conventional DQM while exhibiting a monotonic convergence behavior with respect to the number of sampling points. Furthermore, unlike the conventional DQM, solutions of the proposed method are not very sensitive to the sampling point distribution.

Keywords

Scientia Iranica
Volume 23, Issue 5 - Serial Number 5
Transactions on Mechanical Engineering (B)
October 2016
Pages 2125-2143

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History

  • Receive Date: 09 November 2016
  • Revise Date: 21 December 2024
  • Accept Date: 27 July 2017

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